Question

A straight wire lying in a horizontal plane carries a current of 20 A. (Given, μ0 = 4π × 10-7 Tm/A)
(a) Find the magnitude of the magnetic field at a perpendicular distance of 35 cm from it on the plane. How do you know the direction of the magnetic field?
(b) If the length of the current carrying straight wire is 0.75m and it makes an angle of 60° with the Earth’s magnetic field 6× 10-5 T, find the force experienced by the wire.
(c) Now, ignore the earth’s magnetic field. The wire (carrying 20 A) feels an attractive force of 0.006 N/m due to another parallel wire which lies in the same plane carrying current 25 A. Calculate the distance between these two wires.

Answer 1

The current through the wire is I = 20A and the value permeability of free space is = 4 x 10-7Tm/A.

(a) The magnitude of magnetic filed at a distance x from the straight infinite wire is,

Given x = 35cm = 35 x 10-2m. Therefore,

The direction of magnetic field is found using Right Hand Rule. If right hand thumb is pointing the current, then the curled fingers represent the direction of magnetic field.

(b) The length of the current carrying wire L = 0.75m, the magnetic field B = 6 x 10-5T and the angle that the wire makes with the magnetic filed is 60 degree. The force experienced by the wire is

(c) The second wire carries a current of 25A. The attractive force per unit length of the two wires seperated by a distance x is F = 0.006N/m. Therefore

So the seperation is 0.017m.